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Based on the authors' three decades of teaching experience, Advanced Engineering Mathematics presents the fundamentals and theoretical concepts of the subject in an intelligible and easy-to-understand style. The carefully planned chapters make this book an effective tool for teaching the application of mathematics to engineering and scientific problems.
The book provides graded sets of examples and exercises that help students understand the concepts and an Answers and Hints section for difficult problems. The exercises emphasize theoretical concepts and provide the practice students need to gain the confidence to apply them. Advanced Engineering Mathematics offers a logical and lucid presentation of both theory and problem solving techniques that ensures students will not ett lost in unnecessary details.
Table of Contents
FUNCTIONS OF A REAL VARIABLE Introduction Limits, Continuity, and Differentiability Application of Derivatives and Taylor's Series Integration and its Applications Improper Integrals
FUNCTIONS OF SEVERAL REAL VARIABLES Introduction Functions of Two Varaibles Partial Derivatives Higher Order Partial Derivatives Maximum and Minimum Values of Functions Multiple Integrals
MATRICES AND EIGENVALUE PROBLEMS Introduction Matrices Vector Spaces Solution of General Linear System of Equations Eigenvalue Problems Answers and Hints
ORDINARY DIFFERENTIAL EQUATIONS OF FIRST ORDER Introduction Formation of Differential Equations Solution of a Differential Equation Initial and Boundary Value Problems Solution of Equations in Separable Form Exact First Order Differential Equations Linear First Order Equations Some Special First Order Equations Orthogonal Trajectories of a Given Family of Curves Existence and Uniqueness of Solutions Answers and Hints
LINEAR DIFFERENTIAL EQUATIONS Introduction Solution of Linear Differential Equations Methods for Solution of Linear Equations Solution of Non-Homogenous Linear Equations Operator Methods for Finding Particular Integrals Simultaneous Linear Equations Answers and Hints
SERIES SOLUTION OF DIFFERENTIAL EQUATIONS Introduction Ordinary and Singular Points of an Equation Power Series Solution Series Solution about a Regular Singular Point: Frobenius Method Answers and Hints
LEGENDRE POLYNOMIALS, BESSEL FUNCTIONS AND STURM-LIOUVILLE PROBLEM Introduction Legendre Differential Equation and Legendre Polynomials Bessel's Differential Equation and Bessel's Functions Sturm-Liouville Problem Answers and Hints
LAPLACE TRANSFORMATION Introduction Basic Theory of Laplace Transforms Laplace Transform Solution of Initial Value Problems Translation Theorems (Shifting Theorems) Laplace Transform of Dirac-delta Function and More Properties of Laplace Transforms Laplace Transform of Periodic Functions Laplace Transform Method for the Solution of Some Partial Differential Equations Answers and Hints
FOURIER SERIES, FOURIER INTEGRALS AND FOURIER TRANSFORMS Introduction Fourier Series Fourier Half-Range Series Fourier Integrals Application of Fourier Series: Separation of Variables Solution of Linear Partial Differential Equations Fourier Transforms Answers and Hints
FUNCTIONS OF A COMPLEX VARIABLE: ANALYTIC FUNCTIONS Introduction Complex Number System Sets of Points in the Complex Plane Functions of a Complex Variable Elementary Functions Limits and Continuity Differentiability and Analyticity Harmonic Functions Answers and Hints
INTEGRATION OF COMPLEX FUNCTIONS Introduction Definite Integrals Cauchy Integral Theorem Chauchy Integral Formula Cauchy Integral Formula for Derivatives Answers and Hints
POWER SERIES, TAYLOR AND LAURENT SERIES Introduction Infinite Sequences Infinite Series Power Series Taylor Series Laurent Series Answers and Hints
ZEROS, SINGULARITIES AND RESIDUES Introduction Zeros and Singularities of Complex Functions Residues Evaluation of Contour Integrals Using Residues Evaluation of Real Integrals Using Residues Answers and Hints
BILINEAR TRANSFORMATION AND CONFORMAL MAPPING Introduction Linear and Inverse Transformations Bilinear Transformations Conformal Mapping Answers and Hints
VECTOR DIFFERENTIAL AND INTEGRAL CALCULUS Introduction Parametric Representatives, Continuity and Differentiability of Vector Functions Gradient of a Scalar Field and Directional Derivative Divergence and Curl of a Vector Field Line Integrals and Green's Theorem Surface Area and Surface Integrals Divergence Theorem of Gauss and Stoke's Theorem Answers and Hints
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